Search results for: introductory mathematics

Authors: Ana Maria Reis D'Azevedo Breda, Catarina Maria Neto da Cruz

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The Japanese art of origami provides a rich context for designing exploratory mathematical activities for children and young people. By folding a simple sheet of paper, fascinating and surprising planar and spatial configurations emerge. Equally surprising is the unfolding process, which also produces striking patterns. The procedure of folding, unfolding, and folding again allows the exploration of interesting geometric patterns. When adequately and systematically done, we may deduce some of the mathematical rules ruling origami. As the child/youth folds the sheet of paper repeatedly, he can physically observe how the forms he obtains are transformed and how they relate to the pattern of the corresponding unfolding, creating space for the understanding/discovery of mathematical principles regulating the folding-unfolding process. As part of a 2023 Summer Academy organized by a Portuguese university, a session entitled “Folding, Thinking and Generalizing” took place. Twenty-three students attended the session, all enrolled in the 2nd cycle of Portuguese Basic Education and aged between 10 and 12 years old. The main focus of this session was to foster the development of critical cognitive and socio-emotional skills among these young learners using origami. These skills included creativity, critical analysis, mathematical reasoning, collaboration, and communication. Employing a qualitative, descriptive, and interpretative analysis of data collected during the session through field notes and students’ written productions, our findings reveal that structured origami-based activities not only promote student engagement with mathematical concepts in a playful and interactive but also facilitate the development of socio-emotional skills, which include collaboration and effective communication between participants. This research highlights the value of integrating origami into educational practices, highlighting its role in supporting comprehensive cognitive and emotional learning experiences.

Keywords: skills, origami rules, active learning, hands-on activities

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Authors: Michael Lousis

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Mathematical competence is the great aim of every mathematical teaching and learning endeavour. This can be defined as an idealised conceptualisation of the quality of cognition and the ability of implementation in practice of the mathematical subject matter, which is included in the curriculum, and is displayed only through performance of doing mathematics. The present study gives a clear definition of mathematical competence in the domains of Arithmetic and Algebra that stems from the explanation of the learners’ errors in these domains. The learners, whose errors are explained, were Greek and English participants of a large, international, longitudinal, comparative research program entitled the Kassel Project. The participants’ errors emerged as results of their work in dealing with mathematical questions and problems of the tests, which were presented to them. The construction of the tests was such as only the outcomes of the participants’ work was to be encompassed and not their course of thinking, which resulted in these outcomes. The intention was that the tests had to provide undeviating comparable results and simultaneously avoid any probable bias. Any bias could stem from obtaining results by involving so many markers from different countries and cultures, with so many different belief systems concerning the assessment of learners’ course of thinking. In this way the validity of the research was protected. This fact forced the implementation of specific research methods and theoretical prospects to take place in order the participants’ erroneous way of thinking to be disclosed. These were Methodological Pragmatism, Symbolic Interactionism, Philosophy of Mind and the ideas of Computationalism, which were used for deciding and establishing the grounds of the adequacy and legitimacy of the obtained kinds of knowledge through the explanations given by the error analysis. The employment of this methodology and of these theoretical prospects resulted in the definition of the learners’ mathematical competence, which is the thesis of the present study. Thus, learners’ mathematical competence is depending upon three key elements that should be developed in their minds: appropriate representations, appropriate meaning, and appropriate developed schemata. This definition then determined the development of appropriate teaching practices and interventions conducive to the achievement and finally the entailment of mathematical competence.

Keywords: representations, meaning, appropriate developed schemata, computationalism, error analysis, explanations for the probable causes of the errors, Kassel Project, mathematical competence

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Authors: Pedro Barros, Ana Breda, Eugenio Rocha, M. Isabel Santos

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As visual and spatial awareness develops, children apprehension of the concept of direction, (relative) distance and (relative) location materializes. Here we present the educational inclusive digital game ORIESPA, under development by the Thematic Line Geometrix, for children aged between 6 and 10 years old, aiming the improvement of their visual and spatial awareness. Visual-spatial abilities are of crucial importance to succeed in many everyday life tasks. Unavoidable in the technological age we are living in, they are essential in many fields of study as, for instance, mathematics.The game, set on a 2D/3D environment, focusses in tasks/challenges on the following categories (1) static orientation of the subject and object, requiring an understanding of the notions of up–down, left–right, front–back, higher-lower or nearer-farther; (2) interpretation of perspectives of three-dimensional objects, requiring the understanding of 2D and 3D representations of three-dimensional objects; and (3) orientation of the subject in real space, requiring the reading and interpreting of itineraries. In ORIESPA, simpler tasks are based on a quadrangular grid, where the front-back and left-right directions and the rotations of 90º, 180º and 270º play the main requirements. The more complex ones are produced on a cubic grid adding the up and down movements. In the first levels, the game's mechanics regarding the reading and interpreting maps (from point A to point B) is based on map routes, following a given set of instructions. In higher levels, the player must produce a list of instructions taking the game character to the desired destination, avoiding obstacles. Being an inclusive game the user has the possibility to interact through the mouse (point and click with a single button), the keyboard (small set of well recognized keys) or a Kinect device (using simple gesture moves). The character control requires the action on buttons corresponding to movements in 2D and 3D environments. Buttons and instructions are also complemented with text, sound and sign language.

Keywords: digital game, inclusion, itinerary, spatial ability

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Authors: Arlene Caney, Linda Fellag

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To counter the adverse effect of Covid-19 on college student success, two faculty members at a US community college have used web-based assessment data to improve curricula and, thus, student outcomes. This case study exemplifies how “closing the loop” by analyzing outcome assessments in real time can improve student learning for academically underprepared students struggling during the pandemic. The purpose of the study was to develop ways to mitigate the negative impact of Covid-19 on student success of underprepared college students. Using the Assessment, Evaluation, Feedback and Intervention System (AEFIS) and other assessment tools provided by the college’s Office of Institutional Research, an English professor and a Music professor collected data in skill areas related to their curricula over four semesters, gaining insight into specific course sections and learners’ performance across different Covid-driven course formats—face-to-face, hybrid, synchronous, and asynchronous. Real-time data collection allowed faculty to shorten and close the assessment loop, and prompted faculty to enhance their curricula with engaging material, student-centered activities, and a variety of tech tools. Frequent communication, individualized study, constructive criticism, and encouragement were among other measures taken to enhance teaching and learning. As a result, even while student success rates were declining college-wide, student outcomes in these faculty members’ asynchronous and synchronous online classes improved or remained comparable to student outcomes in hybrid and face-to-face sections. These practices have demonstrated that even high-risk students who enter college with remedial level language and mathematics skills, interrupted education, work and family responsibilities, and language and cultural diversity can maintain positive outcomes in college across semesters, even during the pandemic.

Keywords: AEFIS, assessment, distance education, institutional research center

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Authors: Abimbola Akintounde

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Supporting the social and emotional needs of young adolescents has become an emergent concern for schools around the world. Yet educators remain in a dilemma regarding the optimum approach for integrating social and emotional learning (SEL) into their content area instruction. The purpose of this study was to explore the perception of secondary students regarding their schoolwide SEL interventions. Twenty-four International Baccalaureate students in a final year mathematics course at an American Public Secondary School near Washington D. C. were randomly selected for participation in this study via an online electronic survey. The participants in this study used Likert-scale items to rate the effectiveness of the socio-emotional and character development programs being implemented at their schools. Respondents also ranked their preferred mode of delivery of social and emotional support programs. About 71% of the teenagers surveyed preferred SEL support rendered via interactive team-building activities and games, 42% of the high school students in the study ranked focus group discussions as their preferred format for SEL interventions, while only 13% of the respondents in the study regarded lectures and presentations as their preferred mode of SEL delivery. About one-fourth of the study participants agreed that explicit instruction was critical to enhancing students’ wellness, 79% agreed that SEL programs should foster less teacher talk, while 88% of the students indicated that student engagement was critical to their mental health. Eighty percent of the teenagers surveyed decried that the focus of their school-wide social and emotional programs was poorly prioritized. About two-thirds of the students agreed that social justice and equity issues should be embedded in their schools’ advisory programs. More than half of the respondents agitated for strategies for managing stress and their school workload. About 54% of the respondents also clamored for SEL programs that reinforce emotion regulation and coping strategies for anxiety. Based on the findings of this study, recommendations were proffered for best practices in the design and implementation of effective learner-friendly social and emotional development interventions.

Keywords: SEL, math anxiety, student support, emotion regulation, social awareness, self awareness, self management, relationship building

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Authors: Esther Cabezas-Rivas

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Ordinary differential equations (ODE) are a fundamental part of the curriculum for most engineering degrees, and students typically have difficulties in the subsequent abstract mathematical calculations. To enhance their motivation and profit that they are digital natives, we propose a teamwork project that includes the creation of a video. It should explain how to model mathematically a real-world problem transforming it into an ODE, which should then be solved using the tools learned in the lectures. This idea was indeed implemented with first-year students of a BSc in Engineering and Management during the period of online learning caused by the outbreak of COVID-19 in Spain. Each group of 4 students was assigned a different topic: model a hot water heater, search for the shortest path, design the quickest route for delivery, cooling a computer chip, the shape of the hanging cables of the Golden Gate, detecting land mines, rocket trajectories, etc. These topics should be worked out through two complementary channels: a written report describing the problem and a 10-15 min video on the subject. The report includes the following items: description of the problem to be modeled, detailed obtention of the ODE that models the problem, its complete solution, and interpretation in the context of the original problem. We report the outcomes of this teaching in context and active learning experience, including the feedback received by the students. They highlighted the encouragement of creativity and originality, which are skills that they do not typically relate to mathematics. Additionally, the video format (unlike a common presentation) has the advantage of allowing them to critically review and self-assess the recording, repeating some parts until the result is satisfactory. As a side effect, they felt more confident about their oral abilities. In short, students agreed that they had fun preparing the video. They recognized that it was tricky to combine deep mathematical contents with entertainment since, without the latter, it is impossible to engage people to view the video till the end. Despite this difficulty, after the activity, they claimed to understand better the material, and they enjoyed showing the videos to family and friends during and after the project.

Keywords: active learning, contextual teaching, models in differential equations, student-produced videos

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Authors: Maria Tsouroufli, Andrea Mondokova, Subashini Suresh

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Background: The under-representation of women and consequent failure to fulfil their potential contribution to Science, Technology, Engineering, Maths, and Medicine (STEMM) subjects in the UK is an issue that the Higher Education sector is being encouraged to address. Focus: The aim of this research is to investigate the barriers, facilitators, and incentives that influence diverse groups of women who have embarked upon a related career in STEMM subjects. The project will address a number of interconnected research questions: 1. How do participants perceive the barriers, facilitators and incentives for women in terms of research, teaching and management/leadership at each stage of their development towards forging a career in STEMM? 2. How might gender intersect with ethnicity, pregnancy/maternity and academic grade in the career experiences of women in STEMM? 3. How do participants perceive the example of female role models in emulating them as a career model? 4. How do successful females in STEMM see themselves as role models and what strategies do they employ to promote their careers? 5. How does institutional culture manifest itself as a barrier or facilitator for women in STEMM subjects in the institution? Methodology and Theoretical framework: A mixed-methodology will be employed in a case study of one university. The study will draw on extant quantitative data for context and involve conducting a qualitative inquiry to discover the perceptions of staff and students around the key concepts under study (career progression, sense of belonging and tenure, role-models, personal satisfaction, perceived gender in/equality, institutional culture). The analysis will be informed by an intersectionality framework, feminist and gender theory, and organisational psychology and human resource management perspectives. Implications: Preliminary findings will be collected in 2017. Conclusions will be drawn and used to inform recruitment and retention, and the development and implementation of initiatives to enhance the experiences and outcomes of women working and studying in STEMM subjects in Higher Education.

Keywords: under-representation, women, STEMM subjects, intersectionality

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Authors: Dávid Kovács, Bálint Csanády, Dániel Boros, Iván Ivkovic, Lóránt Nagy, Dalma Tóth-Lakits, László Márkus, András Lukács

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The modeling practice of financial instruments has seen significant change over the last decade due to the recognition of time-dependent and stochastically changing correlations among the market prices or the prices and market characteristics. To represent this phenomenon, the Stochastic Correlation Process (SCP) has come to the fore in the joint modeling of prices, offering a more nuanced description of their interdependence. This approach has allowed for the attainment of realistic tail dependencies, highlighting that prices tend to synchronize more during intense or volatile trading periods, resulting in stronger correlations. Evidence in statistical literature suggests that, similarly to the volatility, the SCP of certain stock prices follows rough paths, which can be described using fractional differential equations. However, estimating parameters for these equations often involves complex and computation-intensive algorithms, creating a necessity for alternative solutions. In this regard, the Fractional Ornstein-Uhlenbeck (fOU) process from the family of fractional processes offers a promising path. We can effectively describe the rough SCP by utilizing certain transformations of the fOU. We employed neural networks to understand the behavior of these processes. We had to develop a fast algorithm to generate a valid and suitably large sample from the appropriate process to train the network. With an extensive training set, the neural network can estimate the process parameters accurately and efficiently. Although the initial focus was the fOU, the resulting model displayed broader applicability, thus paving the way for further investigation of other processes in the realm of financial mathematics. The utility of SCP extends beyond its immediate application. It also serves as a springboard for a deeper exploration of fractional processes and for extending existing models that use ordinary Wiener processes to fractional scenarios. In essence, deploying both SCP and fractional processes in financial models provides new, more accurate ways to depict market dynamics.

Keywords: fractional Ornstein-Uhlenbeck process, fractional stochastic processes, Heston model, neural networks, stochastic correlation, stochastic differential equations, stochastic volatility

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Authors: Denise Levy, Anna Lucia C. H. Villavicencio

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In a rapid-changing world, science teachers face considerable challenges. In addition to the basic curriculum, there must be included several transversal themes, which demand creative and innovative strategies to be arranged and integrated to traditional disciplines. In Brazil, nuclear science is still a controversial theme, and teachers themselves seem to be unaware of the issue, most often perpetuating prejudice, errors and misconceptions. This article presents the authors’ experience in the development of an interdisciplinary pedagogical proposal to include nuclear science in the basic curriculum, in a transversal and integrating way. The methodology applied was based on the analysis of several normative documents that define the requirements of essential learning, competences and skills of basic education for all schools in Brazil. The didactic materials and resources were developed according to the best practices to improve learning processes privileging constructivist educational techniques, with emphasis on active learning process, collaborative learning and learning through research. The material consists of an illustrated book for students, a book for teachers and a manual with activities that can articulate nuclear science to different disciplines: Portuguese, mathematics, science, art, English, history and geography. The content counts on high scientific rigor and articulate nuclear technology with topics of interest to society in the most diverse spheres, such as food supply, public health, food safety and foreign trade. Moreover, this pedagogical proposal takes advantage of the potential value of digital technologies, implementing QR codes that excite and challenge students of all ages, improving interaction and engagement. The expected results include the education of the educators for nuclear science communication in a transversal and integrating way, demystifying nuclear technology in a contextualized and significant approach. It is expected that the interdisciplinary pedagogical proposal contributes to improving attitudes towards knowledge construction, privileging reconstructive questioning, fostering a culture of systematic curiosity and encouraging critical thinking skills.

Keywords: science education, interdisciplinary learning, nuclear science, scientific literacy

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Authors: Linda Dusman, Linda Baker

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The Bearman Study of Audience Engagement examined the potential for real-time music education during online symphony orchestra concerts. It follows on the promising results of a preliminary study of STEAM (Science, Technology, Engineering, Arts, and Mathematics) education during live concerts, funded by the National Science Foundation with the Baltimore Symphony Orchestra. For the Bearman Study, audience groups were recruited to attend two previously recorded concerts of the National Orchestral Institute (NOI) in 2020 or the Utah Symphony in 2021. They used a smartphone app called EnCue to present real-time program notes about the music being performed. Short notes along with visual information (photos and score fragments) were designed to provide historical, cultural, biographical, and theoretical information at specific moments in the music where that information would be most pertinent, generally spaced 2-3 minutes apart to avoid distraction. The music performed included Dvorak Symphony No. 8 and Mahler Symphony No. 5 at NOI, and Mendelssohn Scottish Symphony and Richard Strauss Metamorphosen with the Utah Symphony, all standard repertoire for symphony orchestras. During each phase of the study (2020 and 2021), participants were randomly assigned to use the app to view program notes during the first concert or to use the app during the second concert. A total of 139 participants (67 in 2020 and 72 in 2021) completed three online questionnaires, one before attending the first concert, one immediately after the concert, and the third immediately after the second concert. Questionnaires assessed demographic background, expertise in music, engagement during the concert, learning of content about the composers and the symphonies, and interest in the future use of the app. In both phases of the study, participants demonstrated that they learned content presented on the app, evidenced by the fact that their multiple-choice test scores were significantly higher when they used the app than when they did not. In addition, most participants indicated that using the app enriched their experience of the concert. Overall, they were very positive about their experience using the app for real-time learning and they expressed interest in using it in the future at both live and streaming concerts. Results confirmed that informal real-time learning during concerts is possible and can generate enhanced engagement and interest in classical music.

Keywords: audience engagement, informal education, music technology, real-time learning

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Authors: Noury Bakrim

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Formalization is indeed a foundational Mathematical Linguistics as demonstrated by the pioneering works. While dialoguing with this frame, we nonetheless propone, in our approach of language as a real object, a mathematical linguistics/biosemiotics defined as a dialectical synthesis between induction and computational deduction. Therefore, relying on the parametric interaction of cycles, rules, and features giving way to a sub-hypothetic biological point of view, we first hypothesize a factorial equation as an explanatory principle within Category Mathematics of the Ergobrain: our computation proposal of Universal Grammar rules per cycle or a scalar determination (multiplying right/left columns of the determinant matrix and right/left columns of the logarithmic matrix) of the transformable matrix for rule addition/deletion and cycles within representational mapping/cycle heredity basing on the factorial example, being the logarithmic exponent or power of rule deletion/addition. It enables us to propone an extension of minimalist merge/label notions to a Language Merge (as a computing principle) within cycle recursion relying on combinatorial mapping of rules hierarchies on external Entax of the Event Sequence. Therefore, to define combinatorial maps as language merge of features and combinatorial hierarchical restrictions (governing, commanding, and other rules), we secondly hypothesize from our results feature/hierarchy exponentiation on graph representation deriving from Gromov's Symbolic Dynamics where combinatorial vertices from Fe are set to combinatorial vertices of Hie and edges from Fe to Hie such as for all combinatorial group, there are restriction maps representing different derivational levels that are subgraphs: the intersection on I defines pullbacks and deletion rules (under restriction maps) then under disjunction edges H such that for the combinatorial map P belonging to Hie exponentiation by intersection there are pullbacks and projections that are equal to restriction maps RM₁ and RM₂. The model will draw on experimental biomathematics as well as structural frames with focus on Amazigh and English (cases from phonology/micro-semantics, Syntax) shift from Structure to event (especially Amazigh formant principle resolving its morphological heterogeneity).

Keywords: rule/cycle addition/deletion, bio-mathematical methodology, general merge calculation, feature exponentiation, combinatorial maps, event sequence

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Authors: Gezahegn Bekele Welldgiyorgise

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It is obvious that the economics, politics and social conditions of a country are determined by the quality and standard of its education. Indeed, education plays a vital role in changing the consciousness and awareness of society and transforming it on a large scale. Moreover, education contributes a lot to the advancement of science and technology, information and communication, and above all, it speeds up its progress in no time if it focuses mainly on the qualitative approach to education. Education brings about universal change and transformation and lightens mankind in all dimensions. It creates an educated, enlightened and brightened generation in society. The generation will be sharped, sharpened and well-oriented if it gets modern, sophisticated and standardized education in its field of study. The main goal of education is to produce well-qualified, well-trained and disciplined young offers in a given community. If the youth is well trained and well-mannered, he will certainly be enlightened, problem solvers and solution seekers, researchers, and innovators. In this respect, we have to provide the youth with modern education, a teaching-learning process led by active learning and a participatory approach with a new curriculum preparation for the age of children supported by modern facilities (ICT).In addition to that, the curriculum should have to give attention to mathematics and science lessons that include international experience in a comfortable school and classrooms. Therefore, the generation that will be created through such kinds of the guided education system will make the students active participants, self-confident, researchers and problem solvers, besides that result in changed life standards and a developed country. Similarly, our country, Ethiopia, has aimed to get such change in youth (generation) through modern education, designing a new educational policy and curriculum which was implemented for many years, although the goal of education has not reached the required level. To get the main idea of the article, I should have answered the question of why our country's educational goal had not reached the desired level because it is necessary to lay the foundation for research in finding out problems seen through students learning performance, the first task is selecting primary-school as a sample. Therefore, we selected “Dilla primary school (5-8)” which is a workplace for a teacher and gives me a chance to recognize students’ learning performance to recognize their learning grades (internal and external) and measure performance (achievement) of students easily’.

Keywords: curriculum, performance, innovation, learning

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Authors: Shafaq Rubab

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The primary reason for dropping out of school is associated with students’ lack of motivation in class, especially in mathematics. Digital game-based learning is an approach that is being actively explored; there are very few learning games based on proven instructional design models or frameworks due to which the effectiveness of the learning games suffers. The purpose of this research was twofold: first, developing an appropriate instructional design model and second, evaluating the impact of the instructional design model on students’ motivation. This research contributes significantly to the existing literature in terms of student motivation and the impact of instructional design model in digital game-based learning. The sample size for this study consists of two hundred out-of-school students between the age of 6 and 12 years. The research methodology used for this research was a quasi-experimental approach and data was analyzed by using the instructional material motivational survey questionnaire which is adapted from the Keller Arcs model. Control and experimental groups consisting of two hundred students were analyzed by utilizing instructional material motivational survey (IMMS), and comparison of result from both groups showed the difference in the level of motivation of the students. The result of the research showed that the motivational level of student in the experimental group who were taught by the game was higher than the student in control group (taught by conventional methodology). The mean score of the experimental group against all subscales (attention, relevance, confidence, and satisfaction) of IMMS survey was higher; however, no statistical significance was found between the motivational scores of control and experimental group. The positive impact of game-based learning on students’ level of motivation, as measured in this study, strengthens the case for the use of pedagogically sound instructional design models in the design of interactive learning applications. In addition, the present study suggests learning from interactive, immersive applications as an alternative solution for children, especially in Third World countries, who, for various reasons, do not attend school. The mean score of experimental group against all subscales of IMMS survey was higher; however, no statistical significance was found between motivational scores of control and experimental group.

Keywords: digital game-based learning, students’ motivation, and instructional designing, instructional material motivational survey

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Authors: Sudha T., Naveen C.

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Dengue is a serious public health issue that causes significant annual economic and welfare burdens on nations. However, enhanced optimization techniques and quantitative modeling approaches can predict the incidence of dengue. By advocating for a data-driven approach, public health officials can make informed decisions, thereby improving the overall effectiveness of sudden disease outbreak control efforts. The National Oceanic and Atmospheric Administration and the Centers for Disease Control and Prevention are two of the U.S. Federal Government agencies from which this study uses environmental data. Based on environmental data that describe changes in temperature, precipitation, vegetation, and other factors known to affect dengue incidence, many predictive models are constructed that use different machine learning methods to estimate weekly dengue cases. The first step involves preparing the data, which includes handling outliers and missing values to make sure the data is prepared for subsequent processing and the creation of an accurate forecasting model. In the second phase, multiple feature selection procedures are applied using various machine learning models and optimization techniques. During the third phase of the research, machine learning models like the Huber Regressor, Support Vector Machine, Gradient Boosting Regressor (GBR), and Support Vector Regressor (SVR) are compared with several optimization techniques for feature selection, such as Harmony Search and Genetic Algorithm. In the fourth stage, the model's performance is evaluated using Mean Square Error (MSE), Mean Absolute Error (MAE), and Root Mean Square Error (RMSE) as assistance. Selecting an optimization strategy with the least number of errors, lowest price, biggest productivity, or maximum potential results is the goal. In a variety of industries, including engineering, science, management, mathematics, finance, and medicine, optimization is widely employed. An effective optimization method based on harmony search and an integrated genetic algorithm is introduced for input feature selection, and it shows an important improvement in the model's predictive accuracy. The predictive models with Huber Regressor as the foundation perform the best for optimization and also prediction.

Keywords: deep learning model, dengue fever, prediction, optimization

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Authors: Sonia Saddiqui, Maya Marcus

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UTS STEAMpunk Girls is an educational program for young women (aged 12-16), to empower them to be more informed and active members of the 21st century workforce. With the number of STEM graduates on the decline, especially among young women, an additional aim of the program is to trial a STEAM (Science, Technology, Engineering, Arts/Humanities/Social Sciences, Mathematics), inter-disciplinary approach to improving STEM engagement. In-line with UNESCO’s recent focus on promoting ‘transversal competencies’ in future graduates, the program utilised co-design, project-based learning, entrepreneurial processes, and inter-disciplinary learning. The program consists of two phases. Taking a participatory design approach, the first phase (co-design workshops) provided valuable insight into student perspectives around engaging young women in STEM and inter-disciplinary thinking. The workshops positioned 26 young women from three schools as subject matter experts (SMEs), providing a platform for them to share their opinions, experiences and findings around the STEAM disciplines. The second (pilot) phase put the co-design phase findings into practice, with 64 students from four schools working in groups to articulate problems with real-world implications, and utilising design-thinking to solve them. The pilot phase utilised project-based learning to engage young women in entrepreneurial and STEAM frameworks and processes. Scalable program design and educational resources were trialed to determine appropriate mechanisms for engaging young women in STEM and in STEAM thinking. Across both phases, data was collected via longitudinal surveys to obtain pre-program, baseline attitudinal information, and compare that against post-program responses. Preliminary findings revealed students’ improved understanding of the STEM disciplines, industries and professions, improved awareness of STEAM as a concept, and improved understanding regarding inter-disciplinary and design thinking. Program outcomes will be of interest to high-school educators in both STEM and the Arts, Humanities and Social Sciences fields, and will hopefully inform future programmatic approaches to introducing inter-disciplinary STEAM learning in STEM curriculum.

Keywords: co-design, STEM, STEAM, project-based learning, inter-disciplinary

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Authors: Irfan Ahmed Rind

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Science education has recently become the top priority of government of Pakistan. Number of schemes has been initiated for the improvement of science teaching and learning at primary and secondary levels of education, most importantly training in-service science teachers on inquiry based teaching and learning to empower students and encourage creativity, critical thinking, and innovation among them. Therefore, this approach has been promoted in the recent continuous professional development trainings for the in-service teachers. However, the follow ups on trained science teachers and educators suggest that these teachers fail to implement the inquiry based teaching and learning in their classes. In addition, these trainings also fail to bring any significant change in students’ science content knowledge and understanding as per the annual national level surveys conducted by government and independent agencies. Research suggests that science has been taught using scientific positivism, which supports objectivity based on experiments and mathematics. In contrary, the inquiry based teaching and learning are based on constructivism, which conflicts with the positivist epistemology of science teachers. It was, therefore, assumed that science teachers struggle to implement the inquiry based teaching approach as it conflicts with their basic epistemological beliefs. With this assumption, this research aimed to (i) understand how science teachers conceptualize the nature of science, and how this influence their understanding of learning, learners, their own roles as teachers and their teaching strategies, (ii) identify the conflict of science teachers’ epistemological beliefs with the inquiry based teaching approach, and (iii) find the ways in which science teachers epistemological beliefs may be developed from positivism to constructivism, so that they may effectively use the inquiry based teaching approach in teaching science. Using qualitative case study approach, thirty six secondary and higher secondary science teachers (21 male and 15 female) were selected. Data was collected using interviewed, participatory observations (sixty lessons were observed), and twenty interviews from students for verifications of teachers’ responses. The findings suggest that most of the science teacher were positivist in defining the nature of science. Most of them limit themselves to one fix answer that is provided in the books and that there is only one 'right' way to teach science. There is no room for students’ or teachers’ own opinion or bias when it comes to scientific concepts. Inquiry based teaching seems 'no right' to them. They find it difficult to allow students to think out of the box. However, some interesting exercises were found to be very effective in bringing the change in teachers’ epistemological beliefs. These will be discussed in detail in the paper. The findings have major implications for the teachers, educators, and policymakers.

Keywords: science teachers, epistemology, metacognition, inquiry based teaching

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Authors: Mballa Abanda Luc Aurelien Serge, Henda Gnakate Biba, Kuate Guemo Romaric, Akono Rufine Nicole, Zabotom Yaya Fadel Biba, Petfiang Sidonie, Bella Suzane Jenifer

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The main hypotheses proposed around the definition of the syllable and of music, of the common origin of music and language, should lead the reader to reflect on the cross-cutting questions raised by the debate on the notion of universals in linguistics and musicology. These are objects of controversy, and there lies its interest: the debate raises questions that are at the heart of theories on language. It is an inventive, original, and innovative research thesis. A contribution to the theoretical, musicological, ethno musicological, and linguistic conceptualization of languages, giving rise to the practice of interlocution between the social and cognitive sciences, the activities of artistic creation, and the question of modeling in the human sciences: mathematics, computer science, translation automation, and artificial intelligence. When you apply this theory to any text of a folksong of a world-tone language, you do not only piece together the exact melody, rhythm, and harmonies of that song as if you knew it in advance but also the exact speaking of this language. The author believes that the issue of the disappearance of tonal languages and their preservation has been structurally resolved, as well as one of the greatest cultural equations related to the composition and creation of tonal, polytonal, and random music. The experimentation confirming the theorization, I designed a semi-digital, semi-analog application that translates the tonal languages of Africa (about 2,100 languages) into blues, jazz, world music, polyphonic music, tonal and anatonal music, and deterministic and random music). To test this application, I use music reading and writing software that allows me to collect the data extracted from my mother tongue, which is already modeled in the musical staves saved in the ethnographic (semiotic) dictionary for automatic translation ( volume 2 of the book). The translation is done (from writing to writing, from writing to speech, and from writing to music). Mode of operation: you type a text on your computer, a structured song (chorus-verse), and you command the machine a melody of blues, jazz, and world music or variety, etc. The software runs, giving you the option to choose harmonies, and then you select your melody.

Keywords: language, music, sciences, quantum entenglement

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Authors: Qian Mao, Xiaozan Wang, Jiarong Zhong, Xiaolin Zou

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Introduction: As a result of the decline of students' physical health level and the increase of study pressure, students’ academic performance is not so good. Objective: This study aims to verify whether the Brain-Break intervention in the fourth-grade classroom of primary school can improve students' physical health and academic performance. Methods: According to the principle of no difference in pre-test data, students from two classes of grade four in Fuhai Road Primary School, Fushan district, Yantai city, Shandong province, were selected as experimental subjects, including 50 students in the experimental class (25 males and 25 females) and 50 students in the control class (24 males and 26 females). The content of the experiment was that the students were asked to perform a 4-minute Brain-Berak program designed by the researcher in the second class in the morning and the afternoon, and the intervention lasted for 12 weeks. In addition, the lung capacity, 50-meter run, sitting body forward bend, one-minute jumping rope and one-minute sit-ups stipulated in the national standards for physical fitness of students (revised in 2014) were selected as the indicators of physical health. The scores of Chinese, Mathematics, and English in the unified academic test of the municipal education bureau were selected as the indicators of academic performance. The independent-sample t-test was used to compare and analyze the data of each index between the two classes. The paired-sample t-test was used to compare and analyze the data of each index in the two classes. This paper presents only results with significant differences. Results: in terms of physical health, lung capacity (P=0.002, T= -2.254), one-minute rope skipping (P=0.000, T=3.043), and one-minute sit-ups (P=0.045, T=6.153) were significantly different between the experimental class and the control class. In terms of academic performance, there is a significant difference between the Chinese performance of the experimental class and the control class (P=0.009, T=4.833). Conclusion: Adding Brain-Berak intervention in the classroom can effectively improve the cardiorespiratory endurance (lung capacity), coordination (jumping rope), and abdominal strength (sit-ups) of fourth-grade students. At the same time, it can also effectively improve their Chinese performance. Therefore, it is suggested to promote micro-sports in the classroom of primary schools throughout the country so as to help students improve their physical health and academic performance.

Keywords: academic performance, brain break, fourth grade, physical health

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Authors: Michael Lousis

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This research study is concerned with learner’s errors on Arithmetic and Algebra. The data resulted from a broader international comparative research program called Kassel Project. However, its conceptualisation differed from and contrasted with that of the main program, which was mostly based on socio-demographic data. The way in which the research study was conducted, was not dependent on the researcher’s discretion, but was absolutely dictated by the nature of the problem under investigation. This is because the phenomenon of learners’ mathematical errors is due neither to the intentions of learners nor to institutional processes, rules and norms, nor to the educators’ intentions and goals; but rather to the way certain information is presented to learners and how their cognitive apparatus processes this information. Several approaches for the study of learners’ errors have been developed from the beginning of the 20th century, encompassing different belief systems. These approaches were based on the behaviourist theory, on the Piagetian- constructivist research framework, the perspective that followed the philosophy of science and the information-processing paradigm. The researcher of the present study was forced to disclose the learners’ course of thinking that led them in specific observable actions with the result of showing particular errors in specific problems, rather than analysing scripts with the students’ thoughts presented in a written form. This, in turn, entailed that the choice of methods would have to be appropriate and conducive to seeing and realising the learners’ errors from the perspective of the participants in the investigation. This particular fact determined important decisions to be made concerning the selection of an appropriate framework for analysing the mathematical errors and giving explanations. Thus the rejection of the belief systems concerning behaviourism, the Piagetian-constructivist, and philosophy of science perspectives took place, and the information-processing paradigm in conjunction with the philosophy of mind were adopted as a general account for the elaboration of data. This paper explains why these decisions were appropriate and beneficial for conducting the present study and for the establishment of the ensued thesis. Additionally, the reasons for the adoption of the information-processing paradigm in conjunction with the philosophy of mind give sound and legitimate bases for the development of future studies concerning mathematical error analysis are explained.

Keywords: advantages-disadvantages of theoretical prospects, behavioral prospect, critical evaluation of theoretical prospects, error analysis, information-processing paradigm, opting for the appropriate approach, philosophy of science prospect, Piagetian-constructivist research frameworks, review of research in mathematical errors

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Authors: Wing Mui Winnie So, Tian Luo, Zeyu Han

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To fully explore and develop the potentials of gifted students systematically and strategically by providing them with opportunities to receive education at appropriate levels, schools in Hong Kong are encouraged to adopt the "Three-Tier Implementation Model" to plan and implement the school-based gifted education, with Level Three refers to the provision of learning opportunities for the exceptionally gifted students in the form of specialist training outside the school setting by post-secondary institutions, non-government organisations, professional bodies and technology enterprises. Due to the growing concern worldwide about low interest among students in pursuing STEM (Science, Technology, Engineering, and Mathematics) careers, cultivating and boosting STEM career interest has been an emerging research focus worldwide. Although numerous studies have explored its critical contributors, little research has examined the effectiveness of comprehensive interventions such as “Studying with STEM professional”. This study aims to examine the effect on gifted students’ career interest during their participation in an off-school support programme designed and supervised by a team of STEM educators and STEM professionals from a university. Gifted students were provided opportunities and tasks to experience STEM career topics that are not included in the school syllabus, and to experience how to think and work like a STEM professional in their learning. Participants involved 40 primary school students joining the intervention programme outside the normal school setting. Research methods included adopting the STEM career interest survey and drawing tasks supplemented with writing before and after the programme, as well as interviews before the end of the programme. The semi-structured interviews focused on students’ views regarding STEM professionals; what’s it like to learn with a STEM professional; what’s it like to work and think like a STEM professional; and students’ STEM identity and career interest. The changes in gifted students’ STEM career interest and its well-recognised significant contributors, for example, STEM stereotypes, self-efficacy for STEM activities, and STEM outcome expectation, were collectively examined from the pre- and post-survey using T-test. Thematic analysis was conducted for the interview records to explore how studying with STEM professional intervention can help students understand STEM careers; build STEM identity; as well as how to think and work like a STEM professional. Results indicated a significant difference in STEM career interest before and after the intervention. The influencing mechanism was also identified from the measurement of the related contributors and the analysis of drawings and interviews. The potential of off-school support programme supervised by STEM educators and professionals to develop gifted students’ STEM career interest is argued to be further unleashed in future research and practice.

Keywords: gifted students, STEM career, STEM education, STEM professionals

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Authors: Isabella Lima Leite de Freitas

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The importance of astronomy for humanity is unquestionable. Despite being a robust science, capable of bringing new discoveries every day and quickly increasing the ability of researchers to understand the universe more deeply, scientific research in this area can also help in various applications outside the domain of astronomy. The objective of this study was to review and conduct a descriptive analysis of published studies that presented the importance of astronomy in the area of education. A narrative review of the literature has been performed, considering the articles published in the last five years. As astronomy involves the study of physics, chemistry, biology, mathematics and technology, one of the studies evaluated presented astronomy as the gateway to science, demonstrating the presence of astronomy in 52 school curricula in 37 countries, with celestial movement the dominant content area. Another intervention study, evaluating individuals aged 4-5 years, demonstrated that the attribution of personal characteristics to cosmic bodies, in addition to the use of comprehensive astronomy concepts, favored the learning of science in preschool-age children, considering the use of practical activities of accompaniment and free drawing. Aiming to measure scientific literacy, another study developed in Turkey, motivated the authorities of this country to change the teaching materials and curriculum of secondary schools after the term “astronomy” appeared as one of the most attractive subjects for young people aged 15 to 24. There are also reports in the literature of the use of pedagogical tools, such as the representation of the Solar System on a human scale, where students can walk along the orbits of the planets while studying the laws of dynamics. The use of this tool favored the teaching of the relationship between distance, duration and speed over the period of the planets, in addition to improving the motivation and well-being of students aged 14-16. An important impact of astronomy on education was demonstrated in the study that evaluated the participation of high school students in the Astronomical Olympiads and the International Astronomy Olympiad. The study concluded that these Olympics have considerable influence on students who pursue a career in teaching or research later on, many of whom are in the area of astronomy itself. In addition, the literature indicates that the teaching of astronomy in the digital age has facilitated the availability of data for researchers, but also for the general population. This fact can increase even more the curiosity that the astronomy area has always instilled in people and promote the dissemination of knowledge on an expanded scale. Currently, astronomy has been considered an important ally in strengthening the school curricula of children, adolescents and young adults. This has been used as teaching tools, in addition to being extremely useful for scientific literacy, being increasingly used in the area of education.

Keywords: astronomy, education area, teaching, review

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Authors: Achirawatt Tungsombatsanti, Toansakul Santiboon, Kamon Ponkham

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Strategies of the STEM education was aimed to prepare of an interdisciplinary and applied approach for the instructional of science, technology, engineering, and mathematics in an integrated students for enhancing engagement of their science skills to the Problem-Based Learning (PBL) method in Borabu School with a sample consists of 80 students in 2 classes at the 12th grade level of their learning achievements on electromagnetic issue. Research administrations were to separate on two different instructional model groups, the 40-experimental group was designed with the STEM instructional experimenting preparation and induction in a 40-student class and the controlling group using the PBL was designed to students identify what they already know, what they need to know, and how and where to access new information that may lead to the resolution of the problem in other class. The learning environment perceptions were obtained using the 35-item Physics Laboratory Environment Inventory (PLEI). Students’ creating attitude skills’ sustainable development toward physics were assessed with the Test Of Physics-Related Attitude (TOPRA) The term scaling was applied to the attempts to measure the attitude objectively with the TOPRA was used to assess students’ perceptions of their science attitude toward physics. Comparisons between pretest and posttest techniques were assessed students’ learning achievements on each their outcomes from each instructional model, differently. The results of these findings revealed that the efficiency of the PLB and the STEM based on criteria indicate that are higher than the standard level of the 80/80. Statistically, significant of students’ learning achievements to their later outcomes on the controlling and experimental physics class groups with the PLB and the STEM instructional designs were differentiated between groups at the .05 level, evidently. Comparisons between the averages mean scores of students’ responses to their instructional activities in the STEM education method are higher than the average mean scores of the PLB model. Associations between students’ perceptions of their physics classes to their attitudes toward physics, the predictive efficiency R2 values indicate that 77%, and 83% of the variances in students’ attitudes for the PLEI and the TOPRA in physics environment classes were attributable to their perceptions of their physics PLB and the STEM instructional design classes, consequently. An important of these findings was contributed to student understanding of scientific concepts, attitudes, and skills as evidence with STEM instructional ought to higher responding than PBL educational teaching. Statistically significant between students’ learning achievements were differentiated of pre and post assessments which overall on two instructional models.

Keywords: learning instructional managements, problem-based learning, STEM education, method, enhancement, students learning achievements, science attitude, physics classes

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Authors: Laura Rodriguez Amaya

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Advances in science, technology, engineering, and mathematics (STEM) are viewed as important to countries’ national economies and their capacities to be competitive in the global economy. However, many countries experience low numbers of students entering these disciplines. To strengthen the professional STEM pipelines, it is important that students are retained in these disciplines at universities. Scholars agree that to retain students in universities’ STEM degrees, it is necessary that STEM course content shows the relevance of these academic fields to their daily lives. By increasing students’ understanding on the importance of these degrees and careers, students’ motivation to remain in these academic programs can also increase. An effective way to make STEM content relevant to students’ lives is the use of geospatial technologies and geovisualization in the classroom. The Geospatial Revolution, and the science and technology associated with it, has provided scientists and engineers with an incredible amount of data about Earth and Earth systems. This data can be used in the classroom to support instruction and make content relevant to all students. The purpose of this study was to find out the prevalence use of geospatial technologies and geovisualization as teaching practices in a USA university. The Teaching Practices Inventory survey, which is a modified version of the Carl Wieman Science Education Initiative Teaching Practices Inventory, was selected for the study. Faculty in the STEM disciplines that participated in a summer learning institute at a 4-year university in the USA constituted the population selected for the study. One of the summer learning institute’s main purpose was to have an impact on the teaching of STEM courses, particularly the teaching of gateway courses taken by many STEM majors. The sample population for the study is 97.5 of the total number of summer learning institute participants. Basic descriptive statistics through the Statistical Package for the Social Sciences (SPSS) were performed to find out: 1) The percentage of faculty using geospatial technologies and geovisualization; 2) Did the faculty associated department impact their use of geospatial tools?; and 3) Did the number of years in a teaching capacity impact their use of geospatial tools? Findings indicate that only 10 percent of respondents had used geospatial technologies, and 18 percent had used geospatial visualization. In addition, the use of geovisualization among faculty of different disciplines was broader than the use of geospatial technologies. The use of geospatial technologies concentrated in the engineering departments. Data seems to indicate the lack of incorporation of geospatial tools in STEM education. The use of geospatial tools is an effective way to engage students in deep STEM learning. Future research should look at the effect on student learning and retention in science and engineering programs when geospatial tools are used.

Keywords: engineering education, geospatial technology, geovisualization, STEM

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Authors: Marjorie Miguel

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Globalization offers better career opportunities hence demands more competent professionals efficient for the job. With the transformation of the world industry from competition to collaboration coupled with the rapid development in the field of science and technology, engineers need not only to be technically proficient, but also multilingual-skilled: two characteristics that a global engineer possesses. English often serves as the global language between people from different cultures being the medium mostly used in international business. Ironically, most universities worldwide adapt engineering curriculum heavily built around the language of mathematics not realizing that the goal of an engineer is not only to create and design, but more importantly to promote his creations and designs to the general public through effective communication. This premise led to some developments in the teaching process of English subjects in the tertiary level which include the integration of the technical knowledge related to the area of specialization of the students in the English subjects that they are taking. This is also known as English for Specific Purposes. This study focused on the development of English for Specific Purposes-Based Instructional Materials for Engineering Students of Bulacan State University (BulSU). The materials were tailor-made in which the contents and structure were designed to meet the specific needs of the students as well as the industry. Based on the needs analysis, the needs of the students and the industry were determined to make the study descriptive in nature. The major respondents included fifty engineering students and ten professional engineers from selected institutions. The needs analysis was done and the results showed the common writing difficulties of the students and the writing skills needed among the engineers in the industry. The topics in the instructional materials were established after the needs analysis was conducted. Simple statistical treatment including frequency distribution, percentages, mean, standard deviation, and weighted mean were used. The findings showed that the greatest number of the respondents had an average proficiency rating in writing, and the much-needed skills that must be developed by the engineers are directly related to the preparation and presentation of technical reports about their projects, as well as to the different communications they transmit to their colleagues and superiors. The researcher undertook the following phases in the development of the instructional materials: a design phase, development phase, and evaluation phase. Evaluations are given by some college instructors about the instructional materials generally helped in its usefulness and significance making the study beneficial not only as a career enhancer for BulSU engineering students, but also creating the university one of the educational institutions ready for the new millennium.

Keywords: English for specific purposes, instructional materials, needs analysis, write (right) job description

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Authors: Orhan Akınoğlu, Arif Çömek, Ersin Elmacı, Tuğba Gündoğdu

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The concept map is known to be a powerful tool to organize the ideas and concepts of an individuals’ mind. This tool is a kind of visual map that illustrates the relationships between the concepts of a certain subject. The effect of concept mapping on cognitive and affective qualities is one of the research topics among educational researchers for last decades. We educators want to utilize it both as an instructional tool or an assessment tool in classes. For that reason, this study aimed to determine the effect of concept mapping as a learning strategy in science classes on students’ academic achievement and attitude. The research employed a randomized pre-test post-test control group design. Data collected from 60 sixth grade students participated in the study from a randomly selected primary school in Turkey. Sixth-grade classes of the school were analyzed according to students’ academic achievement, science attitude, gender, mathematics, science courses grades, and their GPAs before the implementation. Two of the classes found to be equivalent (t=0,983, p>0,05) and one of them was defined as experimental and the other one control group randomly. During a 5-weeks period, the experimental group students (N=30) used the paper-based concept mapping method while the control group students (N=30) were taught with the traditional approach according to the science and technology education curriculum for light and sound subject. Both groups were taught by the same teacher who is experienced using concept mapping in science classes. Before the implementation, the teacher explained the theory of the concept maps and showed how to create paper-based concept mapping individually to the experimental group students for two hours. Then for two following hours she asked them to create some concept maps related to their former science subjects and gave them feedback by reviewing their concept maps to be sure that they can create during the implementation. The data were collected by science achievement test, science attitude scale and personal information form. Science achievement test and science attitude scale were implemented as pre-test and post-test while personal information form was implemented just as once. The reliability coefficient of the achievement test was KR20=0,76 and Cronbach’s Alpha of the attitude scale was 0,89. SPSS statistical software was used to analyze the data. According to the results, there was a statistically significant difference between the experimental and control group for academic achievement but not for attitude. The experimental group had significantly greater gains from academic achievement test than the control group (t=0,02, p<0,05). The findings showed that the paper-and-pencil concept mapping can be used as an effective method for students’ academic achievement in science classes. The results have implications for further researches.

Keywords: concept mapping, science education, constructivism, academic achievement, science attitude

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Authors: Amparo Camacho

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ABET accredited programs must assess the development of student learning outcomes (SOs) in engineering programs. Different institutions implement different strategies for this assessment, and they are usually designed “in house.” This paper presents a proposal for including standardized tests to complement the ABET assessment model in an engineering college made up of six distinct engineering programs. The engineering college formulated a model of quality assurance in education to be implemented throughout the six engineering programs to regularly assess and evaluate the achievement of SOs in each program offered. The model uses diverse techniques and sources of data to assess student performance and to implement actions of improvement based on the results of this assessment. The model is called “Assessment Process Model” and it includes SOs A through K, as defined by ABET. SOs can be divided into two categories: “hard skills” and “professional skills” (soft skills). The first includes abilities, such as: applying knowledge of mathematics, science, and engineering and designing and conducting experiments, as well as analyzing and interpreting data. The second category, “professional skills”, includes communicating effectively, and understanding professional and ethnical responsibility. Within the Assessment Process Model, various tools were used to assess SOs, related to both “hard” as well as “soft” skills. The assessment tools designed included: rubrics, surveys, questionnaires, and portfolios. In addition to these instruments, the Engineering College decided to use tools that systematically gather consistent quantitative data. For this reason, an in-house exam was designed and implemented, based on the curriculum of each program. Even though this exam was administered during various academic periods, it is not currently considered standardized. In 2017, the Engineering College included three standardized tests: one to assess mathematical and scientific reasoning and two more to assess reading and writing abilities. With these exams, the college hopes to obtain complementary information that can help better measure the development of both hard and soft skills of students in the different engineering programs. In the first semester of 2017, the three exams were given to three sample groups of students from the six different engineering programs. Students in the sample groups were either from the first, fifth, and tenth semester cohorts. At the time of submission of this paper, the engineering college has descriptive statistical data and is working with various statisticians to have a more in-depth and detailed analysis of the sample group of students’ achievement on the three exams. The overall objective of including standardized exams in the assessment model is to identify more precisely the least developed SOs in order to define and implement educational strategies necessary for students to achieve them in each engineering program.

Keywords: assessment, hard skills, soft skills, standardized tests

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Authors: Michela Quadrini

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Chord diagrams occur in mathematics, from the study of RNA to knot theory. They are widely used in theory of knots and links for studying the finite type invariants, whereas in molecular biology one important motivation to study chord diagrams is to deal with the problem of RNA structure prediction. An RNA molecule is a linear polymer, referred to as the backbone, that consists of four types of nucleotides. Each nucleotide is represented by a point, whereas each chord of the diagram stands for one interaction for Watson-Crick base pairs between two nonconsecutive nucleotides. A chord diagram is an oriented circle with a set of n pairs of distinct points, considered up to orientation preserving diffeomorphisms of the circle. A linear chord diagram (LCD) is a special kind of graph obtained cutting the oriented circle of a chord diagram. It consists of a line segment, called its backbone, to which are attached a number of chords with distinct endpoints. There is a natural fattening on any linear chord diagram; the backbone lies on the real axis, while all the chords are in the upper half-plane. Each linear chord diagram has a natural genus of its associated surface. To each chord diagram and linear chord diagram, it is possible to associate the intersection graph. It consists of a graph whose vertices correspond to the chords of the diagram, whereas the chord intersections are represented by a connection between the vertices. Such intersection graph carries a lot of information about the diagram. Our goal is to define an LCD equivalence class in terms of identity of intersection graphs, from which many chord diagram invariants depend. For studying these invariants, we introduce a new representation of Linear Chord Diagrams based on a set of appropriate topological operators that permits to model LCD in terms of the relations among chords. Such set is composed of: crossing, nesting, and concatenations. The crossing operator is able to generate the whole space of linear chord diagrams, and a multiple context free grammar able to uniquely generate each LDC starting from a linear chord diagram adding a chord for each production of the grammar is defined. In other words, it allows to associate a unique algebraic term to each linear chord diagram, while the remaining operators allow to rewrite the term throughout a set of appropriate rewriting rules. Such rules define an LCD equivalence class in terms of the identity of intersection graphs. Starting from a modelled RNA molecule and the linear chord, some authors proposed a topological classification and folding. Our LCD equivalence class could contribute to the RNA folding problem leading to the definition of an algorithm that calculates the free energy of the molecule more accurately respect to the existing ones. Such LCD equivalence class could be useful to obtain a more accurate estimate of link between the crossing number and the topological genus and to study the relation among other invariants.

Keywords: chord diagrams, linear chord diagram, equivalence class, topological language

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Authors: Henda Gnakate Biba, Ndassa Mouafon Issa

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Dictionaries modeled on the Western model [tonic accent languages] are not suitable and do not account for tonal languages phonologically, which is why the [prosodic and phonological] ethnographic dictionary was designed. It is a glossary that expresses the tones and the rhythm of words. It recreates exactly the speaking or singing of a tonal language, and allows the non-speaker of this language to pronounce the words as if they were a native. It is a dictionary adapted to tonal languages. It was built from ethnomusicological theorems and phonological processes, according to Jean. J. Rousseau 1776 hypothesis /To say and to sing were once the same thing/. Each word in the French dictionary finds its corresponding language, ekaη. And each word ekaη is written on a musical staff. This ethnographic dictionary is also an inventive, original and innovative research thesis, but it is also an inventive, original and innovative research thesis. A contribution to the theoretical, musicological, ethno musicological and linguistic conceptualization of languages, giving rise to the practice of interlocution between the social and cognitive sciences, the activities of artistic creation and the question of modeling in the human sciences: mathematics, computer science, translation automation and artificial intelligence. When you apply this theory to any text of a folksong of a world-tone language, you do not only piece together the exact melody, rhythm, and harmonies of that song as if you knew it in advance but also the exact speaking of this language. The author believes that the issue of the disappearance of tonal languages and their preservation has been structurally resolved, as well as one of the greatest cultural equations related to the composition and creation of tonal, polytonal and random music. The experimentation confirming the theorization designed a semi-digital, semi-analog application which translates the tonal languages of Africa (about 2,100 languages) into blues, jazz, world music, polyphonic music, tonal and anatonal music and deterministic and random music). To test this application, I use a music reading and writing software that allows me to collect the data extracted from my mother tongue, which is already modeled in the musical staves saved in the ethnographic (semiotic) dictionary for automatic translation ( volume 2 of the book). Translation is done (from writing to writing, from writing to speech and from writing to music). Mode of operation: you type a text on your computer, a structured song (chorus-verse), and you command the machine a melody of blues, jazz and, world music or, variety etc. The software runs, giving you the option to choose harmonies, and then you select your melody.

Keywords: music, language, entenglement, science, research

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Authors: John Njikem

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Attention Deficit Hyperactivity Disorder (ADHD) is one of the most commonly diagnosed behavioral disorders in children, associated with this disorder are core symptoms of inattention, hyperactivity and impulsivity. This study was purposely to enlighten and inform teachers, policy makers and other professionals concern in the education of this group of learners in inclusive schools in Buea, Cameroon. The major purpose of this study was to identify children with ADHD in elementary schools practicing inclusive education and to investigate the effect of classroom based intervention on their academic performance. The research problem stems from the fact that majority of children with ADHD in our school mostly have problems with classroom tasks like paying attention, easily distracted, and difficulties in organization and very little has been done to manage this numerous conditions, therefore it was necessary for the researcher to identify them and implement some inclusive strategies that teachers can better use in managing the behavior of this group of learners. There were four research questions and the study; the sample population used for the study was 27 pupils (3-7years old) formally identified with key symptoms of ADHD from primary 3-6 from four primary inclusive schools in Buea. Two sub-types of ADHD children were identified by using the recent DSM-IV behavioral checklist in recording their behavior after teacher and peer nomination they were later subjected to three groups for classroom intervention. Data collection was done by using interviews and other supportive methods such as document consultation, field notes and informal talks as additional sources was also used to gather information. Classroom Intervention techniques were carried out by the teachers themselves for 8 weeks under the supervision of the researcher, results were recorded for the 27 children's academic performance in the areas of math’s, writing and reading. Descriptive Statistics was applied in analyzing the data in percentages while tables and diagrams were used to represent the results. Findings obtained indicated that there was significant increase in the level of attention and organization on classroom tasks in the areas of reading, writing and mathematics. Finding also show that there was a more significant improvement made on their academic performance using the combined intervention approach which was proven to be the most effective intervention technique for pupils with ADHD in the study. Therefore it is necessary that teachers in inclusive primary schools in Buea understand the needs of these children and learn how to identify them and also use this intervention approaches to accommodate them in classroom task in order to encourage inclusive educational classroom practices in the country. Recommendations were based on each research objective and suggestions for further studies centered on other methods of classroom intervention for ADHD children in inclusive settings.

Keywords: attention deficit hyperactivity disorder, inclusive classrooms, academic performance, impulsivity

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Authors: Adisorn Banhan, Toansakul Santiboon, Prasong Saihong

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Using the Socio-Scientific Issues-Based Learning Method is to compare of the blended instruction of STEM education with a sample consisted of 84 students in 2 classes at the 11th grade level in Sarakham Pittayakhom School. The 2-instructional models were managed of five instructional lesson plans in the context of electronic wave issue. These research procedures were designed of each instructional method through two groups, the 40-experimental student group was designed for the instructional STEM education (STEMe) and 40-controlling student group was administered with the Socio-Scientific Issues-Based Learning (SSIBL) methods. Associations between students’ learning achievements of each instructional method and their science attitudes of their predictions to their exploring activities toward physics with the STEMe and SSIBL methods were compared. The Measuring Reasonable Ethics Test (MRET) was assessed students’ reasonable ethics with the STEMe and SSIBL instructional design methods on two each group. Using the pretest and posttest technique to monitor and evaluate students’ performances of their reasonable ethics on electromagnetic wave issue in the STEMe and SSIBL instructional classes were examined. Students were observed and gained experience with the phenomena being studied with the Socio-Scientific Issues-Based Learning method Model. To support with the STEM that it was not just teaching about Science, Technology, Engineering, and Mathematics; it is a culture that needs to be cultivated to help create a problem solving, creative, critical thinking workforce for tomorrow in physics. Students’ attitudes were assessed with the Test Of Physics-Related Attitude (TOPRA) modified from the original Test Of Science-Related Attitude (TOSRA). Comparisons between students’ learning achievements of their different instructional methods on the STEMe and SSIBL were analyzed. Associations between students’ performances the STEMe and SSIBL instructional design methods of their reasonable ethics and their science attitudes toward physics were associated. These findings have found that the efficiency of the SSIBL and the STEMe innovations were based on criteria of the IOC value higher than evidence as 80/80 standard level. Statistically significant of students’ learning achievements to their later outcomes on the controlling and experimental groups with the SSIBL and STEMe were differentiated between students’ learning achievements at the .05 level. To compare between students’ reasonable ethics with the SSIBL and STEMe of students’ responses to their instructional activities in the STEMe is higher than the SSIBL instructional methods. Associations between students’ later learning achievements with the SSIBL and STEMe, the predictive efficiency values of the R2 indicate that 67% and 75% for the SSIBL, and indicate that 74% and 81% for the STEMe of the variances were attributable to their developing reasonable ethics and science attitudes toward physics, consequently.

Keywords: socio-scientific issues-based learning method, STEM education, science attitudes, measurement, reasonable ethics, physics classes

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